In a small, heat-proof glass measuring pitcher or bowl, combine the dried porcini mushrooms and 1 cup boiling water. Let stand for 20 minutes. Remove the mushrooms with a slotted spoon and coarsely chop. Set aside.
Line a fine-mesh sieve with a paper coffee filter or cheesecloth (muslin) and strain the mushroom-soaking liquid to remove the grit; reserve the liquid.
In a large saute or frying pan, heat the olive oil over medium heat. Add the shallots and saute until soft and translucent, 2 to 3 minutes. Add the garlic and saute for 1 minute. Add the shiitake mushrooms and saute until they brown around the edges, 3 to 4 minutes. Stir in the cremini mushrooms, porcini mushrooms, reserved soaking liquid, stock and 1/2 teaspoon of the salt. Cover and cook until the mushrooms are tender, about 5 minutes. Uncover and stir in the butter, chopped thyme, the remaining 1/2 teaspoon salt and the pepper. Set aside and keep warm.
Fill a large pot 3/4 full with water and bring to a boil. Add the linguine and cook until al dente (tender), 8 to 10 minutes, or according to package directions. Drain the pasta thoroughly.
Divide the pasta among warmed individual shallow bowls and top with the mushroom sauce. Garnish with the fresh thyme sprigs.